# Definition:Segment of Circle

## Definition

In the words of Euclid:

*A***segment of a circle**is the figure contained by a straight line and a circumference of a circle.

(*The Elements*: Book $\text{III}$: Definition $6$)

### Base

The **base** of a segment of a circle is the straight line forming one of the boundaries of the seqment.

In the above diagram, $AB$ is the **base** of the highlighted segment.

### Angle of a Segment

In the words of Euclid:

*An***angle of a segment**is that contained by a straight line and a circumference of a circle.

(*The Elements*: Book $\text{III}$: Definition $7$)

That is, it is the angle the base makes with the circumference where they meet.

It can also be defined as the angle between the base and the tangent to the circle at the end of the base:

### Angle in a Segment

In the words of Euclid:

*An***angle in a segment**is the angle which, when a point is taken on the circumference of the segment and straight lines are joined from it to the extremities of the straight line which is the base of the segment, is contained by the straight lines so joined.

(*The Elements*: Book $\text{III}$: Definition $8$)

*And, when the straight lines containing the angle cut off a circumference, the angle is said to***stand upon**that circumference.

(*The Elements*: Book $\text{III}$: Definition $9$)

Such a segment is said to **admit** the angle specified.

### Similar Segments

In the words of Euclid:

**Similar segments of circles**are those which admit equal angles, or in which the angles are equal to one another.

(*The Elements*: Book $\text{III}$: Definition $11$)

### Major Segment

Let $AB$ be a chord of a circle $\CC$ defined by the points $A$ and $B$ on the circumference of $\CC$.

The **major segment** of $\CC$ with respect to $AB$ is the segment between $AB$ and the major arc of $\CC$ between $A$ and $B$.

### Minor Segment

Let $AB$ be a chord of a circle $\CC$ defined by the points $A$ and $B$ on the circumference of $\CC$.

The **minor segment** of $\CC$ with respect to $AB$ is the segment between $AB$ and the minor arc of $\CC$ between $A$ and $B$.

## Also see

- Results about
**segments of circles**can be found**here**.

## Sources

- 1998: David Nelson:
*The Penguin Dictionary of Mathematics*(2nd ed.) ... (previous) ... (next):**segment**:**2.** - 2008: David Nelson:
*The Penguin Dictionary of Mathematics*(4th ed.) ... (previous) ... (next):**segment**:**2.** - 2014: Christopher Clapham and James Nicholson:
*The Concise Oxford Dictionary of Mathematics*(5th ed.) ... (previous) ... (next):**segment**